Proppant mixing and metering system

ABSTRACT

An oilfield material reservoir is disclosed. The oilfield material reservoir has a body, the body having an upper end, a lower end, a sidewall extending between the upper and lower ends, the sidewall defining a recess within the body, an opening defined by the upper end, and a first orifice defined by the lower end. The oilfield material reservoir is also provided with a metering gate connected to the body at the lower end. The metering gate has a base having a second orifice aligned with the first orifice, and a knife gate connected to the base. The second orifice has a substantially trapezoidal shape. The knife gate is configured to slidably cover the second orifice. A method is also disclosed for controlling a discharge rate of oilfield material within the oilfield material reservoir by adjusting a metering open area of the second orifice according to mathematical modeling equations.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims priority to the provisional patentapplication identified by U.S. Ser. No. 61/490,698, filed on May 27,2011, the entire content of which is hereby incorporated herein byreference.

TECHNICAL FIELD

The present disclosure generally relates to systems, methods, and/orapparatus of mixing and metering proppant into fracturing fluid to beinjected into a wellbore.

BACKGROUND

The statements made herein merely provide information related to thepresent disclosure and may not constitute prior art, and may describesome embodiments illustrating the invention.

In hydraulic fracturing, fracturing fluid is injected into a wellbore,penetrating a subterranean formation and forcing the fracturing fluid atpressure to crack and fracture the strata or rock. Proppant is placed inthe fracturing fluid and thereby placed within the fracture to form aproppant pack to prevent the fracture from closing when pressure isreleased, providing improved flow of recoverable fluids, i.e., oil, gas,or water. The success of a hydraulic fracturing treatment is related tothe fracture conductivity which is the ability of fluids to flow fromthe formation through the proppant pack. In other words, the proppantpack or matrix may have a high permeability relative to the formationfor fluid to flow with low resistance to the wellbore. Permeability ofthe proppant matrix may be increased through distribution of proppantand non-proppant materials within the fracture to increase porositywithin the fracture.

Some approaches to hydraulic fracture conductivity have constructedproppant clusters in the fracture, as opposed to constructing acontinuous proppant pack. These methods may alternate the stages ofproppant-laden and proppant-free fracturing fluids to create proppantclusters in the fracture and open channels between them for formationfluids to flow. Thus, the fracturing treatments result in aheterogeneous proppant placement (HPP) and a “room and pillar”configuration in the fracture, rather than a homogeneous proppantplacement and consolidated proppant pack. The amount of proppantdeposited in the fracture during each HPP stage is modulated by varyingfluid transport characteristics, such as viscosity and elasticity; theproppant densities, diameters, and concentrations; and the fracturingfluid injection rate.

Proppant placement techniques based on the fracture geometry have beendeveloped for use during traditional proppant pack operations. However,proppant placement in HPP is considerably more challenging and the artis still in search of ways to improve the proppant placement techniquesin HPP operations.

Prior to injection of the fracturing fluid, the proppant and othercomponents of the fracturing fluid may be blended. The current state oftechnology for enabling existing blending equipment for performing HPPand slickwater fracturing operations relies on the use of automaticproppant concentration control based on proppant metering gatepercentage opening in a gravity-fed system. Automatic proppantconcentration control based on densitometer feedback is the mostcommonly used mode for proppant metering in conventional fracturingwork, but cannot be used in certain applications due to excessively slowdensitometer response times. Additionally, current gate designs inexisting blending equipment generally have irregular metering orificegeometries with respect to gate percentage opening that do not allowhighly accurate and consistent proppant flow control. A means forachieving consistent, well-behaved proppant metering due to consistent,well-behaved metering orifice geometry for optimal performance isdesirable.

Many proppant addition systems use one or more augers to supply proppantor a mixture of proppant and fluids, such as slickwater, gels, orhydrocarbons. In these systems, the proppant may be delivered to thefracturing fluid, pumps, or mixer from an oilfield material reservoir,commonly called a proppant hopper or receiver. The auger meters theproppant volumes and rates into a fluid stream or mixer. The auger maymeter the proppant by calculating the known amount of proppant an augermay move at a given auger speed in revolutions per minute (rpm). Thedensity of fracturing fluid including the proppant therefore may bedetermined, in auger systems, based on the rpm at which the auger isoperating in combination with the density of the fracturing fluiddetermined prior to the addition of the proppant. Auger systems mayrequire a larger area in order to accommodate an auger capable ofproviding a sufficient volume of proppant to the mixer or the fluidstream.

An alternative to the auger fed proppant addition systems is the use ofa gravity fed proppant addition system. Gravity fed proppant additionsystems may transfer proppant via gravity free fall to a mixer in orderto be added to fracturing fluid. Metering the proppant volume in agravity fed system may be calculated by determining the flow rate of theproppant through an orifice of a known size, often called a meteringgate, when the proppant is in gravity free fall through the orifice.Gravity fed systems may also employ the use of pressurization to aid intransferring proppants into the fluid stream or mixer. Pressurizationmethods in gravity fed systems may include pressurizing the proppantcontainer subject to the gravity feed or utilizing a venturi effectwhere a smaller diameter pipe is connected to a larger diameter pipe todraw the proppant from the proppant container into the mixer or fluidstream. Gravity fed systems may require a smaller area, as they may notemploy an auger.

Gravity fed proppant addition systems may use automatic proppantconcentration control based on the orifice of a known size. Blendingequipment has been adapted for slickwater fracturing jobs by use ofautomatic proppant concentration control based on the metering gatepercentage opening in the gravity fed proppant addition system. Thisautomatic proppant concentration control may be calledAuto-Concentration in Gate Percentage Mode. Automatic proppantconcentration control may be based on densitometer feedback; however,densitometer feedback may not be an effective control mechanism forslickwater applications due to the inability of densitometers todifferentiate between the density of low proppant concentration slurriescommon to slickwater fracturing and the density of the base fluidcarrier itself.

SUMMARY

This summary is provided to introduce a selection of concepts that arefurther described below in the detailed description. This summary is notintended to identify key or essential features of the claimed subjectmatter, nor is it intended to be used as an aid in limiting the scope ofthe claimed subject matter.

According to one aspect of the present disclosure, at least oneembodiment relates to an oilfield material reservoir. In this aspect,the oilfield material reservoir has a body, and a metering gate. Thebody has an upper end, a lower end, and a sidewall extending between theupper end and the lower end. The sidewall defines a recess within thebody. An opening is defined by the upper end, and a first orifice isdefined by the lower end. The metering gate is connected to the body atthe lower end thereof, and has a base having a second orifice alignedwith the first orifice, and a knife gate connected to the base. Thesecond orifice has a substantially trapezoidal shape. The knife gate isconfigured to slidably cover the second orifice.

According to another aspect of the present disclosure, at least oneembodiment relates to a method for controlling a discharge rate of anoilfield material within the oilfield material reservoir by adjusting ametering open area of the second orifice according to mathematicalmodeling equations. In this method, an oilfield material reservoir isprovided with an opening for receiving an oilfield material and a firstorifice for discharging the oilfield material. A metering gate isprovided at the first orifice for controlling the discharge rate of theoilfield material by adjusting the metering gate according to the set ofequations taking into consideration a metering open area of the meteringgate, a height of the second orifice of the metering gate, a top lengthof the second orifice of the metering gate, a bottom length of thesecond orifice of the metering gate, and a height of the metering openarea of the metering gate. The equations may also consider a baselineoilfield material flow rate and a constant for the baseline oilfieldmaterial. The equations may also consider, in controlling the meteringgate, a desired mass flow rate for the actual oilfield material used, aparticle size factor affecting flow rate for the actual oilfieldmaterial, a particle geometry factor affecting flow rate for the actualoilfield material, a particle texture factor affecting flow rate for theactual oilfield material, a particle coating factor affecting flow ratefor the actual oilfield material, an environmental vibration factoraffecting flow rate for the actual oilfield material, an environmentalmoisture factor affecting flow rate for the actual oilfield material, aspecific gravity for the actual oilfield material, and a specificgravity for the baseline oilfield material on which the baselineoilfield material is determined.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of a system and method for mixing and metering oilfieldmaterial are described with reference to the following figures. The samenumbers are used throughout the figures to reference like features andcomponents. Implementations of various technologies will hereafter bedescribed with reference to the accompanying drawings. However, itshould be understood that the accompanying drawings illustrate thevarious implementations described herein and are not meant to limit thescope of various technologies described herein.

FIG. 1 shows a perspective view of a blending unit with two oilfieldmaterial reservoirs constructed in accordance with an embodiment of thepresent disclosure.

FIG. 2 shows a perspective view of the oilfield material reservoirconstructed in accordance with an embodiment of the present disclosure.

FIG. 3 shows a perspective view of one of the oilfield materialreservoirs of FIG. 1.

FIG. 4 shows a partial, top plan view of a base having a second orificepartially covered by a knife gate in accordance with an embodiment ofthe present disclosure.

DETAILED DESCRIPTION

At the outset, it should be noted that in the development of any suchactual embodiment, numerous implementation-specific decisions will bemade to achieve the developer's specific goals, such as compliance withsystem related and business related constraints, which will vary fromone implementation to another. Moreover, it will be appreciated thatsuch a development effort might be complex and time consuming but wouldnevertheless be a routine undertaking for those of ordinary skill in theart having the benefit of this disclosure. In addition, the compositionused/disclosed herein can also comprise some components other than thosecited. In the summary and this detailed description, each numericalvalue should be read once as modified by the term “about” (unlessalready expressly so modified), and then read again as not so modifiedunless otherwise indicated in context. Also, in the summary and thisdetailed description, it should be understood that a concentration rangelisted or described as being useful, suitable, or the like, is intendedto include any concentration within the range, including the end points,is to be considered as having been stated. For example, “a range of from1 to 10” is to be read as indicating each possible number along thecontinuum between about 1 and about 10. Thus, even if specific datapoints within the range, or even no data points within the range, areexplicitly identified or refer to a few specific, it is to be understoodthat inventors appreciate and understand that any data points within therange are to be considered to have been specified, and that inventorspossessed knowledge of the entire range and all points within the range.

Referring now to FIG. 1, shown therein is a blending unit 10 with twooilfield material reservoirs, or hoppers 12, constructed in accordancewith the inventive concepts disclosed herein. The blending unit 10 maybe mounted on a trailer or skid to facilitate injection of oilfieldmaterial into a wellbore. Two hoppers 12 a and 12 b are shown, with eachhopper 12 having a body 14 configured to receive an oilfield material,such as a proppant.

For purposes of conciseness, the term “oilfield material” as used hereinmay include proppant, but may also include and should not be limited to,dry guar, cement, suspending agents of the type used in drilling mud,such as polymers, clays, emulsions, transition metal oxides andhydroxides, as will be appreciated by a person skilled in the art.

The term “proppant” as used herein relates to sized particles mixed withfracturing fluid to provide an efficient conduit for production of fluidfrom the reservoir to the wellbore. For example, the term “proppant” asused herein may include extramatrical channel-forming materials,referred to as channelant, and also may include naturally occurring sandgrains or gravel, man-made or specially engineered proppants, such asresin-coated sand or high-strength ceramic materials like sinteredbauxite. Proppant materials may also include fibers. The fibers can be,for example, glass, ceramics, carbon including carbon-based compounds,metal including metallic alloys, or the like, or a combination thereof,or a polymeric material such as PLA, PGA, PET, polyol, or the like, or acombination thereof.

Referring to FIGS. 1-2, the body 14 of the hopper 12 has an upper end16, a lower end 18, and a sidewall 20 extending between the upper end 16and the lower end 18. The sidewall 20 defines a recess 22 within thebody 14 of the hopper 12. The upper end 16 of the body 14 defines anopening 24 for receiving the proppant, and the lower end 18 of the body14 defines a first orifice 26 for discharging the proppant. Connected tothe lower end 18 of the body 14 is a metering gate 28 which may be usedto control the discharge rate of the proppant to a mixer (not shown).

The sidewall 20 of the body 14 may be configured with a first side 30and a second side 32 which taper from the upper end 16 to the lower end18. As shown in FIGS. 1-2, the first side 30 and second side 32 maytaper from substantially near the upper end 16 of the body 14 to thelower end 18 of the body 14. The tapering of the first side 30 andsecond side 32 may facilitate directing a flow of proppant from theopening 24, through the recess 22, to the first orifice 26. Althoughshown in FIGS. 1-2 with the first side 30 and second side 32 astapering, it will be understood that one or more sides of the sidewall20 of the body 14 may be tapered between the upper end 16 and the lowerend 18 to facilitate the flow of proppant from the opening 24, throughthe recess 22, to the orifice 26. The flow of proppant through therecess 22 and first orifice 26 may be a gravity-fed flow where proppanttravels through the first orifice 26 by gravity to the mixer.

The first orifice 26, defined by the lower end 18 of the body 14, mayform the shape of a trapezoid, triangle, square, rectangle, or otherpolynomial. The area of the first orifice 26 may be manipulated with themetering gate 28 connected to the lower end 18 of the body 14.Manipulating the area of the first orifice 26 may allow for the proppantflow rate to be regulated through the first orifice 26. Regulation ofthe flow rate may involve the creation of a mathematical model where theproppant rate may be expressed as a function of factors representing theeffects of physical proppant properties and environmental factors toachieve a desired flow rate of proppant in gravity free fall through thefirst orifice 26, as will be discussed in more detail below.

The metering gate 28 connected to the lower end 18 of the body 14 maycomprise a base 34 connected to the lower end 18 of the body 14, asecond orifice 35 formed within the base 34, a knife gate 36 connectedto the base 34 and configured to slidably cover the first orifice 26and/or the second orifice 35, and an actuator 38 connected to the base34 and the knife gate 36 configured to cause the knife gate 36 toslidably cover the second orifice 35. The second orifice 35, formedwithin the base 34, can be substantially trapezoidal in shape andoverlaps the first orifice 26 of the body 14 of the hopper 12, such thatwhen the knife gate 36 slidably covers the second orifice 35, the knifegate 36 also slidably covers the first orifice 26. The base 34 may beconnected to the lower end 18 by brazing, welding, bolting, or any othersuitable means of connection. The knife gate 36 may be connected to thebase 34 by brackets 40 a and 40 b, as shown in FIG. 2, and with aplurality of rollers 42. The knife gate 36 may be mounted between thebrackets 40 a and 40 b and between the plurality of rollers 42 and thebase 34, so as to secure the knife gate 36 against the base 34. Theknife gate 36, mounted between the plurality of rollers 42 and the base34 may then slidably move beneath the base 34 so as to slidably coverthe second orifice 35. The actuator 38 may be mechanically connected tothe base 34 and the knife gate 36 via any suitable method such that theactuator 38 may articulate the knife gate 36 between completely coveringthe second orifice 35, completely uncovering the second orifice 35, andany level of partial coverage therebetween.

The actuator 38 may be implemented as a pneumatic cylinder, hydrauliccylinder, electric cylinder, or any other actuator 38 suitable to causethe knife gate 36 to slidably cover the second orifice 35. As shown inFIGS. 1-3, the actuator 38 may be implemented as a hydraulic cylinderconnected to the base 34 by a housing 43 and connected to the knife gate36 at a piston head 44. The actuator 38 may articulate the knife gate 36between open, close, and intermittent positions of closure of the secondorifice 35 by extending or retracting a piston 46. Extending andretracting the piston 46 of the actuator 38 may be performed by sendingelectrical signals through a control unit 48 electrically connected to acomputer, processor, controller, or other electronic device capable ofsending and receiving data indicative of instructions for articulatingthe knife gate 36.

The hopper 12 may also be provided with piping 50 through the sidewall20 in communication with a mixer (not shown) below the hopper 12. Thepiping 50 may also be provided in communication with the recess 22 ofthe hopper 12. The piping 50 may be connected to a dry additive feeder52 such that dry additive chemicals from the dry additive feeder 52 maybe discharged through the piping 50 passing through the sidewall 20 ofthe hopper 12 and into the mixer. The piping 50 may also discharge dryadditive chemicals into the hopper 12, such that the dry additivechemicals are discharged from the dry additive feeder 52, into thepiping 50, and into the recess 22, thereby flowing with the proppantinto the mixer through the first and second orifices 26 and 35,respectively.

FIG. 3 illustrates the hopper 12 as provided with a chute 62 extendingalong an exterior surface of the body 14 of the hopper 12. The chute 62may have a connection to the body 14 formed via bolts, welding, brazing,or any other suitable method. The chute 62 may be in communication withan inlet 63 (see FIG. 2) leading to the mixer disposed below the hopper12 and chute 62. The chute 62 may enable disbursement of a non-proppantadditive, such as a fiber, to the mixer through the inlet. The inlet mayreceive the non-proppant additive from the chute 62 and the proppantfrom the hopper 12, or the mixer may have a plurality of inlets throughwhich the nonproppant additive and the proppant individually flow.

Referring now to FIG. 4, in operation, the proppant flow rate can beregulated and predicted through a metering orifice geometry whileaccounting for certain physical proppant characteristics andenvironmental factors that affect flow rate such as particle massdensity, particle size, flow factors accounting for geometry (e.g.,roundness, angularity, shape irregularity, etc.), flow factorsaccounting for surface texture (e.g., roughness, smoothness, etc.), flowfactors accounting for surface coatings (e.g., cured or partially curedresinous coatings), vibration from surroundings, moisture, etc. Themetering orifice geometry may be applied, considering the abovecharacteristics, to determine and automatically articulate the knifegate 36 to enable a desired size of the second orifice 35 by at leastpartially covering the first and second orifices 26 and 35 with theknife gate 36.

The regulation and prediction of proppant flow rate may involve thecreation of a model in a mathematical form that allows proppant flowrate to be expressed as a function of factors representing the effectsof the foregoing listed physical proppant properties and environmentalfactors applied to the metering orifice geometry whose area, deemeddirectly proportional to flow rate, can be expressed in a form thatwould allow the prediction of how much of the orifice geometry wouldneed to be open to achieve a desired flow rate of proppant in gravityfree fall.

The geometry of the first and second orifices 26 and 35, respectively,may be implemented in a trapezoidal shape, as shown in FIGS. 2 and 3.The area of a trapezoid can be expressed in such a way as to make thepercentage of opening of the first and second orifices 26 and 35 theindependent variable in a second degree polynomial formulation. Afteraccounting for the effects on proppant flow from the foregoing listedenvironmental and physical proppant properties, the resulting model mayallow the required gate percentage opening to be solved using aquadratic equation when presented with a required proppant metering ratefor a desired proppant concentration and downhole slurry rate. Themetering orifice geometry model therefore may form a basis for anautomatic proppant control system for heterogeneous proppant placementoperations and slickwater applications.

FIG. 6 illustrates one example of the second orifice 35 in the currentapplication. The equation for the area of a trapezoid can be expressedas:

$\begin{matrix}{Y = {{\underset{\underset{2}{\_}}{L\left( {B - A} \right)}\left( {X/L} \right)^{2}} + {{LA}\left( {X/L} \right)}}} & \left( {{Equation}\mspace{14mu} I} \right)\end{matrix}$which is a second degree polynomial with X/L as the independentvariable. Although the present disclosure discusses the second orifice35 in terms of a trapezoidal shape, it will be understood by thoseskilled in the art that this equation is also applicable to the secondorifice 35 where the second orifice 35 is in the shape of otherpolynomials such as a triangle, a square, or a rectangle, for example.

A metering open area Y may be created with specific dimensional valuesassigned for the parameters A, B, and L, and used in conjunction withthe knife gate 36 that travels along the span L of the second orifice35, then X/L represents the fraction of the knife gate 36 span along Lat which the second orifice 35 may be open for proppant flow through themetering open area Y at gate position X. The metering open area Y can bedefined by the second orifice 35 in the base 34 of the metering gate 28and a front edge 70 of the knife gate 36. Additionally, X/L whenexpressed as a percentage may also be known as the knife gate 72percentage of opening.

For a given oilfield material, such as a proppant, chosen to serve as abaseline, the proppant flow rate P_(baseline) through the metering openarea Y can be expressed as the metering open area Y multiplied by aproportionality entity C_(baseline) such that:

$\begin{matrix}{P_{baseline} = {{C_{baseline}Y} = {C_{baseline}\left\lbrack {{\underset{\underset{2}{\_}}{L\left( {B - A} \right)}\left( {X/L} \right)^{2}} + {{LA}\left( {X/L} \right)}} \right\rbrack}}} & \left( {{Equation}\mspace{14mu}{II}} \right)\end{matrix}$with C_(baseline) having units of mass flow rate per unit of meteringopen area Y, and having the form of a function that inherently accountsfor the following for the specific baseline proppant and existingconditions: particle mass density; particle size; flow factorsaccounting for geometry (e.g., roundness, angularity, shapeirregularity, etc.); flow factors accounting for surface texture (e.g.,roughness, smoothness, etc.); flow factors accounting for surfacecoatings (e.g., cured or partially cured resinous coatings); vibrationfrom surroundings; and moisture, etc., for example.

To further expand the model to allow for flow rate predictions for othertypes of proppants with physical properties that may differ from thebaseline proppant, the following factors can be applied to P_(baseline)to yield the following:

$\begin{matrix}{Z_{proppant} = {{F_{size}F_{geometry}F_{texture}F_{coating}F_{vibration}{F_{moisture}\left( {{SG}_{{proppant}\;}/{SG}_{baseline}} \right)}P_{baseline}} = {F_{size}F_{geometry}F_{texture}F_{coating}F_{vibration}{F_{moisture}\left( {{SG}_{{proppant}\;}/{SG}_{baseline}} \right)}{C_{baseline}\left\lbrack {{\underset{\underset{2}{\_}}{L\left( {B - A} \right)}\left( {X/L} \right)^{2}} + {{LA}\left( {X/L} \right)}} \right\rbrack}}}} & \left\lbrack {{Equation}\mspace{14mu}{III}} \right)\end{matrix}$

The variable Z_(proppant) may be equal to a desired mass flow rate for agiven proppant. F_(size) may be equal to a particle size factoraffecting flow rate for a given proppant. F_(geometry) may be equal to aparticle geometry factor affecting flow rate for a given proppant.F_(texture) may be equal to a particle texture factor, for instance aparticle surface texture, affecting flow rate for a given proppant.F_(coating) may be equal to a particle coating factor, for instance aparticle surface coating, affecting flow rate for a given proppant.F_(vibration) may be equal to an environmental vibration factoraffecting flow rate for a given proppant. F_(moisture) may be equal toan environmental moisture factor affecting flow rate for a givenproppant. SG_(proppant) may be equal to a specific gravity for a givenproppant. Finally, SG_(baseline) may be equal to a specific gravity forthe baseline proppant on which P_(baseline) is founded

The foregoing equation can be arranged in the form of:K ₁ x ² +K ₂ x+K ₃=0  (Equation IV)such that:

$K_{1} = {F_{size}F_{geometry}F_{texture}F_{coating}F_{vibration}{F_{moisture}\left( {{SG}_{{proppant}\;}/{SG}_{baseline}} \right)}{C_{baseline}\left\lbrack {{\underset{2}{\underset{\_}{\left. {L\left( {B - A} \right)} \right\rbrack}}K_{2}} = {{F_{size}F_{geometry}F_{texture}F_{coating}F_{vibration}{F_{moisture}\left( {{SG}_{{proppant}\;}/{SG}_{baseline}} \right)}C_{baseline}{LA}K_{3}} = {{{- Z_{proppant}}x} = {X/L}}}} \right.}}$

The factors F_(size), F_(geometry), F_(texture), F_(coating),F_(vibration), and F_(moisture) may be generally empirically determinedand may be arrived at through a proper design of experiments methodologyin conjunction with assumptions that may help simplify the process inachieving a reasonably accurate model.

Once the parameters K₁ and K₂ are arrived at, and knowing the requiredproppant rate Z_(proppant) desired to achieve a specific proppantconcentration at a specific downhole slurry rate, then the required gatefractional opening X/L can be solved for using the quadratic equation:

$\begin{matrix}{x = \frac{{- K_{2}} + \left( {K_{2}^{2} - {4K_{1}K_{3}}} \right)^{1/2}}{2K_{I}}} & \left( {{Equation}\mspace{14mu} V} \right)\end{matrix}$

As shown in FIG. 2, the hopper 12 may also include a control system 76.In general, the control system 76 is provided with the actuator 38 andone or more computer 78. The actuator 38 may be implemented aspreviously described above. The computer 78 may include one or moreprocessor, one or more non-transitory computer readable medium, one ormore input devices, and one or more output devices. The one or moreprocessor may be implemented as a single processor or multipleprocessors working together to execute computer executable instructions.Embodiments of the one or more processors include a digital signalprocessor, a central processing unit, a microprocessor, a multi-coreprocessor, and combinations thereof. The one or more processor may becoupled to the one or more non-transitory computer readable medium andcapable of communicating with the one or more non-transitory computerreadable medium via a path, which may be implemented as a data bus, forexample. The one or more processor may be capable of communicating withthe input device and the output device via paths similar to the pathdescribed above coupling the one or more processor to the one or morenon-transitory computer readable medium. The one or more processor mayalso be capable of interfacing and/or communicating with one or morenetworks via a communications device such as by exchanging electronic,digital, and/or optical signals via the communications device using anetwork protocol such as TCP/IP. It is to be understood that in certainembodiments using more than one processor, the one or more processor maybe located remotely from one another, locating in the same location, orcomprising a unitary multicore processor. The one or more processor maybe capable of reading and/or executing computer executable instructionsand/or creating, manipulating, altering, and storing computer datastructures into the one or more non-transitory computer readable medium.

The one or more non-transitory computer readable medium stores computerexecutable instructions and may be implemented as any conventionalnon-transitory computer readable medium, such as random access memory(RAM), a hard drive, a DVD-ROM, a BLU-RAY, a floppy disk, an opticaldrive, and combinations thereof. When more than one non-transitorycomputer readable medium is used one or more non-transitory computerreadable medium may be located in the same physical location as the oneor more processor, and one or more non-transitory computer readablemedium may be located in a remote physical location from the one or moreprocessor. The physical location of the one or more non-transitorycomputer readable medium can be varied, and one or more non-transitorycomputer readable medium may be implemented as a “cloud memory,” i.e.one or more non-transitory computer readable medium which is partially,or completely based on or accessed using the network, so long as atleast one of the one or more non-transitory computer readable medium islocated local to the one or more processor.

The computer executable instructions stored on the one or morenon-transitory computer readable medium may comprise logic representingEquations I-V, described in relation to FIG. 4 above, for expressing themetering open area Y of the second orifice 35 and the proppant flowrate. The computer may cause the actuator 38 to extend the piston 46 tocover more of the second orifice 35 thereby reducing the size of themetering open area Y or retract the piston 46 to cover less of thesecond orifice 35 thereby increasing the size of the metering openingarea Y. The computer may cause piston 46 to extend and retract based oninputs from a user terminal connected to the computer 78, orautomatically based on sensors within the hopper 12 providing datarelated to the proppant factors of Equation III.

The preceding description has been presented with reference to someembodiments. Persons skilled in the art and technology to which thisdisclosure pertains will appreciate that alterations and changes in thedescribed structures and methods of operation can be practiced withoutmeaningfully departing from the principle, and scope of thisapplication. Accordingly, the foregoing description should be read asconsistent with and as support for the following claims, which are tohave their fullest and fairest scope.

The scope of patented subject matter is defined by the allowed claims.Moreover, the claim language is not intended to invoke paragraph six of35 USC § 112 unless the exact words “means for” are used. The claims asfiled are intended to be as comprehensive as possible, and no subjectmatter is intentionally relinquished, dedicated, or abandoned.

What is claimed is:
 1. An oilfield material reservoir, comprising: abody, the body having an upper end, a lower end, a sidewall extendingbetween the upper end and the lower end, the sidewall defining a recesswithin the body, an opening defined by the upper end, and a firstorifice defined by the lower end; a metering gate connected to the bodyat the lower end, the metering gate comprising a base having a secondorifice and a knife gate connected to the base, the knife gateconfigured to slidably cover the second orifice, wherein the secondorifice overlaps with the first orifice; and a control system comprisingan actuator and a computer, the actuator adapted to move the knife gaterelative to the second orifice, wherein the actuator is controlled bythe computer controlling a discharge rate of an oilfield material byadjusting the knife gate in accordance with an equation: $\begin{matrix}{Y = {{\underset{\underset{2}{\_}}{L\left( {B - A} \right)}\left( {X/L} \right)^{2}} + {{LA}\left( {X/L} \right)}}} & \left( {{Equation}\mspace{14mu} I} \right)\end{matrix}$ wherein: Y represents an opening area of the meteringgate; L represents a height of the second orifice of the metering gate;A represents a top length of the second orifice of the metering gate; Brepresents a bottom length of the second orifice of the metering gate;and X represents a height of the opening area of the metering gate, andwherein logic for the equation is stored on the computer.
 2. Theoilfield material reservoir of claim 1, wherein the second orifice has asubstantially trapezoidal shape.
 3. The oilfield material reservoir ofclaim 1, wherein the second orifice has a substantially rectangularshape.
 4. The oilfield material reservoir of claim 1, wherein the secondorifice has a substantially triangular shape.
 5. The oilfield materialreservoir of claim 1, wherein the actuator retracts to slidably coverthe second orifice with the knife gate, and extends to slidably uncoverthe second orifice.
 6. The oilfield material reservoir of claim 1,wherein the actuator is a hydraulic cylinder.
 7. The oilfield materialreservoir of claim 1, wherein the body has a chute extending along anexterior surface of the body, the chute being in communication with therecess of the body through an opening formed within the sidewall of thebody, the chute configured to enable disbursement of an additive to amixer.
 8. A method, comprising: providing a hopper having an opening forreceiving an oilfield material and a first orifice for discharging theoilfield material; providing a metering gate at the first orifice, themetering gate having a second orifice overlapping with the firstorifice; and controlling a discharge rate of the oilfield material byadjusting a metering open area of the second orifice in accordance withequation: $\begin{matrix}{Y = {{\underset{\underset{2}{\_}}{L\left( {B - A} \right)}\left( {X/L} \right)^{2}} + {{LA}\left( {X/L} \right)}}} & \left( {{Equation}\mspace{14mu} I} \right)\end{matrix}$ wherein: Y represents the metering open area of themetering gate; L represents a height of the second orifice of themetering gate; A represents a top length of the second orifice of themetering gate; B represents a bottom length of the second orifice of themetering gate; and X represents a height of a metering open area of themetering gate.
 9. The method of claim 8, wherein said first and secondorifice cooperate to form a substantially trapezoidal shape.
 10. Themethod of claim 8, wherein said first and second orifice cooperate toform a substantially triangular shape.
 11. The method of claim 8,wherein said first and second orifice cooperate to form a substantiallyrectangular shape.
 12. The method of claim 8, wherein the hopper isgravity fed.
 13. The method of claim 8, further comprising: determininga baseline oilfield material flow rate in accordance with equation:$\begin{matrix}{{P_{baseline} = {{C_{baseline}Y} = {C_{baseline}\left\lbrack {{\underset{\underset{2}{\_}}{L\left( {B - A} \right)}\left( {X/L} \right)^{2}} + {{LA}\left( {X/L} \right)}} \right\rbrack}}};} & \left( {{Equation}\mspace{14mu}{II}} \right)\end{matrix}$ wherein: P_(baseline) represents the baseline oilfieldmaterial flow rate; and C_(baseline) represents a constant for thebaseline oilfield material.
 14. The method of claim 13, furthercomprising determining Cbaseline by considering one or morecharacteristics of the baseline oilfield material.
 15. The method ofclaim 13, wherein characteristics of the baseline oilfield material areselected from the group consisting of particle mass density, particlesize, particle geometry, particle surface texture, particle surfacecoating, vibration from surroundings, and moisture.
 16. The method ofclaim 13, further comprising constructing an actual oilfield materialflow rate equation:Z _(oilfield material) =F _(Size) F _(geometry) F _(texture) F_(coating) F _(vibration) F _(moisture)(SG _(oilfield material) /SG_(baseline))P _(baseline)   (Equation 111); wherein:Z_(oilfield material) represents a desired mass flow rate for the actualoilfield material; F_(size) represents a particle size factor affectingflow rate for the actual oilfield material; F_(geometry) represents aparticle geometry factor affecting flow rate for the actual oilfieldmaterial; F_(texture) represents a particle texture factor affectingflow rate for the actual oilfield material; F_(coating) represents aparticle coating factor affecting flow rate for the actual oilfieldmaterial; F_(vibration) represents an environmental vibration factoraffecting flow rate for the actual oilfield material; F_(moisture)represents an environmental moisture factor affecting flow rate for theactual oilfield material; SG_(oilfield material) represents a specificgravity for the actual oilfield material; SG_(baseline) represents aspecific gravity for the baseline oilfield material on whichP_(baseline) is determined.
 17. The method of claim 16, furthercomprising determining a fractional opening x=X/L of the metering gatein accordance with equation: $\begin{matrix}{{x = \frac{{- K_{2}} + \left( {K_{2}^{2} - {4K_{1}K_{3}}} \right)^{1/2}}{2K_{I}}}{{wherein}\text{:}}{{K_{1} = {F_{size}F_{geometry}F_{texture}F_{coating}F_{vibration}{F_{moisture}\left( {{SG}_{{{oilfield}\mspace{14mu}{material}}\;}/{SG}_{baseline}} \right)}{C_{baseline}\left\lbrack \underset{\underset{2}{\_}}{L\left( {B - A} \right)} \right\rbrack}}};}{{K_{2} = {F_{size}F_{geometry}F_{texture}F_{coating}F_{vibration}{F_{moisture}\left( {{SG}_{{{oilfield}\mspace{14mu}{material}}\;}/{SG}_{baseline}} \right)}C_{baseline}{LA}}};{and}}{K_{3} = {- {Z_{{oilfield}\mspace{14mu}{material}*}.}}}} & \left( {{Equation}\mspace{14mu} V} \right)\end{matrix}$